Oxygen/Combustibles balance (
Lambda ), is calculated from the measured values of O2, CO, CO2, HC, NOx and
Water Vapour in the exhaust gas. This is a direct measurement of Air/Fuel
ratio, and may be easily used to assess fuel mixture balance. The Lambda
calculation compares all of the Oxygen in the exhaust gases to all of the
Carbon and Hydrogen in the gases. ( Water, which contains both Hydrogen and
Oxygen, is determined by estimation using the fraction of the sum of CO to
CO2 in the exhaust.)

The result of the calculation is
‘Lambda’, a dimensionless term that relates nicely to the Stoichiometric
value of air to fuel. At the Stoichiometric point, Lambda = 1.000. A Lambda
value of 1.050 is 5.0% lean, and a Lambda value of 0.950 is 5.0% rich. Once
Lambda is calculated, A/F Ratio can be easily determined by simply
multiplying Lambda times the Stoichiometric A/F ratio for the fuel used -
e.g. 14.71 for petrol - gasoline.

Details of the
Lambda Calculation:

The Brettshneider equation is the
de-facto standard method used to calculate the normalised Air/Fuel Balance
(Lambda) for domestic and International Inspection Programs. It's derived
from a paper written by Dr. J. Brettshneider in 1979. He established a
method to calculate Lambda ( Balance of Oxygen to Fuel ) by comparing the
ratio of Oxygen molecules to Carbon molecules in the exhaust.

Although this equation is very
complex, the result of it is relatively easy to use in practice. Lambda
directly reflects the ‘degree of lean-ness’ of the air/fuel mixture and is
independent how efficiently the fuel is oxidized, a very important factor to
consider when dealing specifically with air / fuel balance issues. The
manner in which this equation is to be used is strictly a function of the
application though, and it is an excellent replacement for "old" commonly
used conventions, such as CO measurement for rich-side applications
(performance tuning), ‘wide range lambda sensors’, which are not only very
non-linear, but also very sensitive to combustibles in the exhaust stream.
The only dependable air/fuel ratio measurement that we have found to date is
one that first makes an accurate measure of the constituent gases in the
exhaust stream (at least the four gases of HC, CO, CO2 and O2) and
calculates the oxygen and combustibles content and then the Lambda and A/F
value.

Using Lambda as
an Diagnostic Aid

It is important to actually use
Lambda in practice to see how well it correlates to the real world. A little
experience here goes a long way in building confidence as to the efficacy of
this parameter!

It is possible to use Lambda as an
aid when tuning an engine provided that the engine is in good running order.

Using Lambda alone however, it is
not enough to diagnose particular emission related problem. Having 4 or 5
Gas Analyser at your disposal is an invaluable tool for engine diagnostics.

Here are some general guide lines.

Lambda - Low - <1.0

Lambda - High - >1.0

Lambda - High - >1.0

Lambda = 1.0

CO = High

CO = Low

CO = Low

CO = Low

CO2 = Low

CO2 = Low

CO2 = Low

CO2 = High

HC = High

HC = Low

HC = High

HC = Low

O2 = Low

O2 = High

O2 = High

O2 = Low

Rich Mixture

Exhaust Leak

Lean Mixture

Tuned

Typical Emission Values With and Without Catalytic
Converter ( good system - guide lines only )

CO

CO2

HC

O2

Lambda

AFR

With Catalyst

0,5 % or less

14,5 % or more

50 ppm or less

0,5 % or less

0,97 - 1,03

14,3:1 to 15,1:1

Without Catalyst

1,5 % or less

13 % or more

250 ppm or less

0,5 % - 2 %

0,90 - 1,10

13,2:1 to 16,2:1

Typical Emission Values Measured Before and After the
Catalytic Converter ( good system - guide lines only )

CO

CO2

HC

O2

Lambda

AFR

Before Catalyst

0,6 %

14,7 %

100 ppm

0,7 %

1,0

14,7

After Catalyst

0,1 %

15,2%

15 ppm

0,1 %

1,0

14,7

The effect of
various ‘octane’ fuel mixes on Lambda:

Various mixes of gasoline contain
differing ratios of short and long hydrocarbon chains, resulting in a variation
of octane rated fuels. This has a small effect on the ratio of hydrogen to
carbon in the fuel, but these variations have a trivial effect on the lambda
calculation! So before you blame your Gas Analyser for the Lambda = "rubbish",
make sure you actually know what fuel ( or mixture of fuels !) is the engine
running on! An difficult task to achieve, so if everything else looks normal,
then the improbable must be the truth! Trust your equipment!

The effect of
Oxygenated fuels on Lambda:

Oxygenated fuels release oxygen
contained a very small amount of oxygen in the fuel, which is released as the
fuel is burned. The total O2 equivalence in typical oxygenated fuel is on the
order of 0.1% O2, so this effect is small.

The effect of NOx
on Lambda:

NOx has a relatively immaterial effect
on the Lambda calculation, as 1,000 ppm NOx is only equivalent to 0.05% Oxygen
utilization. A 4-gas analyzer is adequate for Lambda calculation - but at least
4 gases must be measured. At idle NOx is typically close to 0 ppm so it can be
ignored. At fast Idle and light load, this gas analyser replaces the NOx value
with an "automatic replacement equation", so as close as possible results are
achieved even with 4 gas analyser! Using 5 Gas Analyser however is the ultimate
way to go.

Sample Dilution and
Air Injection Effects on Lambda:

As a side note, it is important to
understand the effect that sampling air leaks or outright Air Injection may have
on Lambda calculation. The percentage of extra air in the exhaust gases will
result in the same percentage error in the Lambda calculation. I.E, a 5% air
leak will not only dilute (lower) the CO, HC, CO2 and NOx gas readings by 5%,
but will increase the Oxygen reading by about 1.00% (5% of 20.9%) and will
result in the calculated Lambda being 5% leaner than it should. That means that
a perfect Lambda of 1.000 will be reported as 1.050 if there is 5% Air Leak or
Injection.

This is a significant error, and can
occur relatively easily. It should be noted that air leaks or injection will
always bias the lambda calculation toward the lean side so they should be dealt
with and corrected before any lambda calculations using measured gases are
attempted. Air injection should be disabled for Lambda to be calculated
correctly.

Engine Misfire &
the effect of Combustion Efficiency on Lambda:

Because the Lambda calculation
determines the Balance between Oxygen and Combustible Gases by comparing all the
oxygen available to the combustibles bearing gases it is relatively insensitive
to the degree to which the combustibles have been oxidised. Thus, an engine
misfire has absolutely no effect on the Lambda calculation!

Pre and Post
Catalytic Converter gases:

Because the Lambda calculation determines the Balance between Oxygen and
Combustible Gases by comparing all the oxygen available to the combustibles
bearing gases, it is relatively insensitive to the degree to which the
combustibles have been oxidised. Thus, the gas stream before a catalytic
converter should calculate the same Lambda value as the gases after a catalytic
converter.

In
essence, because ALL of the gases are used in the Lambda calculation, the gas
mix in the intake manifold, half-way through the combustion process, before a
catalytic converter, or at the tailpipe should ALL yield the same Lambda result.
The intake manifold will contain Oxygen, HC, and no CO, CO2, or NOx. They will,
however be in balance. The tailpipe should contain low levels of Oxygen and HC
and CO (the sources of combustion), but high levels of CO2 and Water Vapour.
They will be at the same balance as the intake manifold gases. Nothing is
lost or gained, just converted! It really does not matter where the gases are
measured, or how efficient the combustion process is!